{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 13\n",
    "\n",
    "# 对称矩阵的特征值分解\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b277079-d724-4050-b087-44272f0e991a",
   "metadata": {},
   "source": [
    "这段代码使用特征值分解展示矩阵 $A$ 对单位圆和向量的逐步变换效果。初始几何形状是单位圆和两个相互垂直的向量，通过应用矩阵 $A$ 及其特征值分解逐步变换，观察其形变过程。\n",
    "\n",
    "首先，代码生成单位圆和两个方向的向量，以 $(x_1, x_2)$ 平面上的单位圆和一对初始基向量 $V_{\\text{vec}} = \\begin{bmatrix} \\frac{\\sqrt{2}}{2} & -\\frac{\\sqrt{2}}{2} \\\\ \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2} \\end{bmatrix}$ 为基础。然后，定义对称矩阵 $A = \\begin{bmatrix} 1.25 & -0.75 \\\\ -0.75 & 1.25 \\end{bmatrix}$，计算其特征值分解 $A = V \\Lambda V^T$，得到特征值对角矩阵 $\\Lambda$ 和特征向量矩阵 $V$，其中 $\\Lambda$ 表示沿特征向量方向的拉伸程度，$V$ 表示变换的旋转方向。\n",
    "\n",
    "接下来，代码逐步展示以下几个变换过程：\n",
    "1. **初始单位圆和向量**：绘制未变换的单位圆和基向量。\n",
    "2. **$A$ 变换**：直接对单位圆应用矩阵 $A$，展示其整体变换效果。此变换体现了 $A$ 在各方向上的旋转和拉伸效果。\n",
    "3. **$V^T$ 变换**：将单位圆和向量与特征向量矩阵 $V^T$ 相乘，将圆和向量转至特征值方向，使后续变换可以沿特征方向操作。\n",
    "4. **$\\Lambda V^T$ 变换**：再对结果应用特征值对角矩阵 $\\Lambda$，展示特征方向上不同缩放系数的影响。\n",
    "5. **$V \\Lambda V^T$ 变换**：将矩阵 $V$ 应用于已缩放的形状，将其旋转回初始坐标系，完成完整变换。\n",
    "\n",
    "通过特征值分解，矩阵 $A$ 的变换被分解为旋转、拉伸、再旋转的步骤，使得每一步的几何效果得以清晰展示，最终的结果与直接应用 $A$ 变换的效果一致，体现了特征值分解的几何意义。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d39652d0-aca8-411c-bc1e-1f69550262a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入数值计算库\n",
    "import matplotlib.pyplot as plt  # 导入绘图库"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cea76571-8443-4531-9987-2aa546b3b50f",
   "metadata": {},
   "source": [
    "## 定义可视化函数 visualize，用于绘制圆和变换向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "760ef65a-c436-4491-803f-95c723f2e184",
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize(X_circle, X_vec, title_txt):  # 绘制输入圆和变换后的向量，显示标题\n",
    "    fig, ax = plt.subplots()  # 创建绘图\n",
    "    plt.plot(X_circle[0, :], X_circle[1, :], 'k', linestyle='--', linewidth=0.5)  # 绘制原始圆\n",
    "\n",
    "    plt.quiver(0, 0, X_vec[0, 0], X_vec[1, 0],  # 绘制第一个向量\n",
    "               angles='xy', scale_units='xy', scale=1,\n",
    "               color=[0, 0.4392, 0.7529])\n",
    "\n",
    "    plt.quiver(0, 0, X_vec[0, 1], X_vec[1, 1],  # 绘制第二个向量\n",
    "               angles='xy', scale_units='xy', scale=1,\n",
    "               color=[1, 0, 0])\n",
    "\n",
    "    plt.axvline(x=0, color='k', zorder=0)  # 绘制 y 轴\n",
    "    plt.axhline(y=0, color='k', zorder=0)  # 绘制 x 轴\n",
    "\n",
    "    plt.ylabel('$x_2$')  # y 轴标签\n",
    "    plt.xlabel('$x_1$')  # x 轴标签\n",
    "\n",
    "    ax.set_aspect(1)  # 设置坐标比例\n",
    "    ax.set_xlim([-2.5, 2.5])  # x 轴范围\n",
    "    ax.set_ylim([-2.5, 2.5])  # y 轴范围\n",
    "    ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 添加网格线\n",
    "    ax.set_xticks(np.linspace(-2, 2, 5))  # 设置 x 轴刻度\n",
    "    ax.set_yticks(np.linspace(-2, 2, 5))  # 设置 y 轴刻度\n",
    "    plt.title(title_txt)  # 设置标题\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f1d81e1-38f4-4411-9c4d-ff652cddfc34",
   "metadata": {},
   "source": [
    "## 绘制原始单位圆和向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "98df156d-6cb1-4e67-b53b-7176802bed4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = np.linspace(0, 2 * np.pi, 100)  # 创建角度数组\n",
    "\n",
    "circle_x1 = np.cos(theta)  # 计算圆 x 方向坐标\n",
    "circle_x2 = np.sin(theta)  # 计算圆 y 方向坐标\n",
    "\n",
    "V_vec = np.array([[np.sqrt(2) / 2, -np.sqrt(2) / 2],  # 定义初始向量矩阵\n",
    "                  [np.sqrt(2) / 2, np.sqrt(2) / 2]])\n",
    "\n",
    "X_circle = np.array([circle_x1, circle_x2])  # 创建单位圆矩阵\n",
    "\n",
    "visualize(X_circle, V_vec, 'Original')  # 绘制原始单位圆和向量\n",
    "\n",
    "## 定义矩阵 A\n",
    "A = np.array([[1.25, -0.75],  # 定义 2x2 非对称矩阵 A\n",
    "              [-0.75, 1.25]])\n",
    "\n",
    "visualize(A @ X_circle, A @ V_vec, '$A$')  # 绘制 A 变换后的圆和向量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cc3a6ed-bd99-4c17-b3af-53bf61c2954b",
   "metadata": {},
   "source": [
    "## 特征值分解 A = V @ D @ V.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2120ab75-c65b-4d62-8551-50636e50f69b",
   "metadata": {},
   "outputs": [],
   "source": [
    "lambdas, V = np.linalg.eig(A)  # 获取 A 的特征值和特征向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8abf62b6-ed8e-493c-a900-5d56d86a587d",
   "metadata": {},
   "outputs": [],
   "source": [
    "D = np.diag(np.flip(lambdas))  # 创建特征值对角矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b4f90069-cf5e-434d-a127-5f1dea69c9f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "V = V.T  # 将特征向量矩阵转置以便变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7d646575-c95e-460a-a33f-04ed00c7c5ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== LAMBDA ===\n",
      "[[0.5 0. ]\n",
      " [0.  2. ]]\n"
     ]
    }
   ],
   "source": [
    "print('=== LAMBDA ===')  # 输出特征值矩阵\n",
    "print(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3e3b6f3a-85b8-48eb-b832-c17677fa376f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== V ===\n",
      "[[ 0.70710678 -0.70710678]\n",
      " [ 0.70710678  0.70710678]]\n"
     ]
    }
   ],
   "source": [
    "print('=== V ===')  # 输出特征向量矩阵\n",
    "print(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "08710e1d-b990-4690-8a46-01a660a50db5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(V.T @ X_circle, V.T @ V_vec, '$V^T$')  # 绘制 V.T 变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "569fad5c-cc53-4eef-9d6a-ad91ffdd1ec1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(D @ V.T @ X_circle, D @ V.T @ V_vec, '$\\u039BV^T$')  # 绘制 D @ V.T 变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "49682d44-8bf7-4223-9366-9a9123fa87a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(V @ D @ V.T @ X_circle, V @ D @ V.T @ V_vec, '$V\\u039BV^T$')  # 绘制 V @ D @ V.T 变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d36a5e44-9eb4-4102-843d-a47713510e8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(A @ X_circle, A @ V_vec, '$A$')  # 绘制 A 变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
